- #1
lockedup
- 70
- 0
Homework Statement
Draw the set of points in the complex plane satisfying the equation |z + 3i| = 4
lockedup said:Homework Statement
Draw the set of points in the complex plane satisfying the equation |z + 3i| = 4
Homework Equations
The Attempt at a Solution
I don't know what z is supposed to be. In class, we've been using z to stand for a complex number (x + yi). Am I supposed to substitute that into the equation? Or, am I supposed to treat z like any real number and find the absolute value?
The equation represents a complex number, z, added to the imaginary number 3i, which equals the real number 4.
The equation represents a circle on a graph, with a radius of 4 units and a center at (-3,0).
To draw a set of points for the equation, you can plot all the points that lie on the circle with a radius of 4 and a center at (-3,0).
Yes, a complex equation can have more than one solution. In the case of "z+3i=4", there are infinitely many points that satisfy the equation and lie on the circle.
Complex equations are used in a variety of fields, such as engineering, physics, and economics, to model and solve problems involving quantities with both real and imaginary components. For example, in electrical engineering, complex equations are used to analyze circuits with both resistance and reactance. In physics, they are used to describe the behavior of waves and oscillations. And in economics, they are used in calculating interest rates and exchange rates.